The role of gentle algebras in higher homological algebra

被引：1

作者：

Haugland, Johanne ^{[1
]}

Jacobsen, Karin M. ^{[3
]}

Schroll, Sibylle ^{[1
,2
]}

机构：

[1] NTNU, Dept Math Sci, N-7491 Trondheim, Norway

[2] Univ Cologne, Dept Math, D-50931 Cologne, Germany

[3] Aarhus Univ, Dept Math, Ny Munkegade 118, DK-8000 Aarhus C, Denmark

来源：

FORUM MATHEMATICUM | 2022年 / 34卷 / 05期

基金：

英国工程与自然科学研究理事会;

关键词：

Gentle algebra; higher homological algebra; d-cluster tilting subcategory; d-abelian category; (d+2)-angulated category; REPRESENTATION-FINITE ALGEBRAS; TILTED ALGEBRAS; STABLE CATEGORIES; AUSLANDER; EXTENSIONS; MODULES;

D O I：

10.1515/forum-2021-0311

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the role of gentle algebras in higher homological algebra. In the first part of the paper, we show that if the module category of a gentle algebra Lambda contains a d-cluster tilting subcategory for some d >= 2, then. is a radical square zero Nakayama algebra. This gives a complete classification of weakly d-representation finite gentle algebras. In the second part, we use a geometric model of the derived category to prove a similar result in the triangulated setup. More precisely, we show that if D-b(Lambda) contains a d-cluster tilting subcategory that is closed under [ d], then Lambda is derived equivalent to an algebra of Dynkin type A. Furthermore, our approach gives a geometric characterization of all d-cluster tilting subcategories of D-b(Lambda) that are closed under [d].

引用

页码：1255 / 1275

页数：21

共 57 条

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